Using probabilistic methods for solving the problem of ensuring leak tightness of heat exchanger tubes of nuclear power plant steam generators - Probabilistic Safety Assessment for Optimum Nuclear Power Plant Life Management (PLiM) - page 286

rate, the time to crack nucleation and the maximum size of the crack with
a simple equation for the crack growth rate.
To calculate the probability of failure or estimate the size of a leak
one must know the number of actual defects and the distribution of their
sizes. However, these data differ from regular ISI data for the defects in
steam generator tubes which results in insufficient reliability of inspection,
detection of defects and their sizes. A simple method, which includes the
use of the Monte Carlo method, was developed for estimating the actual
number of cracks on the basis of the ISI results.
Figure 9.12 illustrates the procedure used in the proposed statistical
model to estimate crack growth. The model is used to estimate the number
of cracks and their size distribution at the end of the i i-th cycle of operation
using data from the i i-th cycle of ISI. Statistical features of crack nucleation
and crack growth rate are represented by statistical distribution functions
whose parameters are derived from statistical analysis of ISI.
The number of actual cracks in steam generator tubes is estimated
using the results of ISI and data on the reliability of quality control, more
precisely, the probability of detecting a defect (PDD). Since the water
chemistry regime (WCR) may vary during operation, WCR assessment
and determination of the actual number of cracks were performed for each
cycle of operation. The actual number of cracks was determined and their
numbers at the end of this cycle predicted at the beginning of the i i-th cycle
of operation. The forecast was then compared with the results of ISI carried
out at the end of the i i-th cycle.

Rate of crack growth

The crack growth rate, used in the simulation, was calculated statistically
according to the ISI data. Figure 9.13 shows data on the rate of crack
growth in the pipes of the steam generator, model F (FPG) in Korea. These
steam generators were in operation for 12.38 effective operating years
(EOY 12.38 during which 12 full-scale inspections were carried out. The
crack growth rate for the i i-th inspection was obtained by dividing the
increment of crack length during the time between the i -th and ( i +1)-th
inspections. The units of increment of crack length were in millimetres, time
in EOY, respectively. Many point in Fig. 9.13 show a negative crack growth
rate which is physically impossible. The negative growth of cracks is due
to unreliable ISI.
Figure 9.14 shows the dimensions of cracks measured in each ISI. It
may be noted that the crack length does not increase in some case. To
obtain non-negative and more precise estimates of the crack growth rate it
was necessary to carry out regression analysis of the crack length for each
cycle of ISI using polynomial approximation. Some regression analysis
results are given in Fig. 9.15. The linear regression equation is used when
the number of points is less than 4. However, when the number of points is

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